In-plane elastic buckling strength of parabolic arch ribs subjected symmetrical loading

When the in-plane flexural rigidity is small in relation to the applied load, the arch ribs may buckle to the in-plane direction. Designers should therefore determine the in-plane buckling strength. To determine the buckling strength of arch ribs, designers have to consider the material nonlinear response. But in the case of arch ribs having large slenderness ratio, arch ribs may buckle in the elastic range, and when the arch ribs have low slenderness ratio, elastic buckling strength is useful in the preliminary design. In this paper, elastic buckling strength of arch ribs, which are frequently used in practical design, is studied using nonlinear finite element method. In general, the relation between flexural rigidity and elastic buckling strength is linear. As seen from the results, however, when the arch ribs have low slenderness ratio, the relation between flexural rigidity and elastic buckling strength is nonlinear.